**or**another event.

## A Single Coin Toss

A single coin toss can be shown on a tree diagram.The probability of each event can be read from each branch:- The probability of getting
**Heads**is.^{1}⁄_{2} - The probability of getting
**Tails**is.^{1}⁄_{2}

**Heads or Tails**.The probability of

**Heads or Tails**is found by adding their probabilities.

^{1}⁄

_{2}+

^{1}⁄

_{2}= 1

## How to Find the Probability of an Event __or__ Another Event on a Tree Diagram

The addition rule can be used for more complicated tree diagrams.
The tree diagram below is for a double coin toss.## Question

What is the probability of both tosses landing the same side up?**or**another event, add

*across*the branches.

## Step-by-Step:

## 1

Find the event given in the question.
The event is the coin landing the same side up on both tosses. There are two ways this can happen:

**Heads and Heads****Tails and Tails**

**Heads and Heads**. These are the top branches and the bottom branches of the tree diagram.__or__Tails and Tails## 2

Use the multiplication rule to find the probabilities of the outcomes.
Multiply the probabilities

For

*along*the branches.For

**Heads and Heads**:
P(Heads and Heads) =

For ^{1}⁄_{2}×^{1}⁄_{2}=^{1}⁄_{4}**Tails and Tails**:
P(Tails and Tails) =

^{1}⁄_{2}×^{1}⁄_{2}=^{1}⁄_{4}## 3

Add the probabilities for these outcomes.

^{1}⁄

_{4}×

^{1}⁄

_{4}=

^{2}⁄

_{4}

## 4

Simplify the fraction if possible. (The fraction in our example is already as simple as possible).
Simplify the fraction by dividing the top and bottom numbers by their greatest common factor (which is 2).

2 ÷ 2 = 1
4 ÷ 2 = 2

## Answer:

The probability of getting**Heads and Heads**is

__or__Tails and Tails^{1}⁄

_{2}. We can also express this as a number (0.5) or a percentage (50%).

## What Is Probability?

A probability is a measure of how likely (how*probable*) an event is to happen. A probability is expressed as a number between 0 (impossible) and 1 (certain). The formula for finding a probability is shown below:

## Top Tip

## A Useful Check

There is a useful way to check that the probabilities on a tree diagram are all correct. The probabilities of each final outcome add up to 1:## You might also like...

probabilitymultiplication rule on a tree diagramunderstanding dependent events on a tree diagramstatistics curriculum

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